In recent years, gas fuel such as natural gas is adopted as one of the alternative fuels to gasoline or light oil. In case that the gas fuel is applied for the internal combustion engine of a vehicle, as disclosed in JP 2000-337208A, such a gas fuel supply system is known for example that a high-pressure cylinder (fuel tank) filled up with the compressed natural gas is mounted on the vehicle, and the gas fuel supplied from the high-pressure cylinder is decompressed with a regulator and then injected into an intake pipe of the internal combustion engine by an injector.
A conventional gas fuel supply system will now be described with reference to FIG. 6.
As shown in the figure, a regulator 61 for decompressing and regulating the pressure of the gas fuel is connected to a high-pressure fuel supply passage 60 connected to a fuel tank (not shown). A low-pressure fuel supply passage 62 is connected to an outlet side of the regulator 61, and the low-pressure fuel supply passage 62 is connected to an injector 64 provided in an intake pipe 63 of the engine.
The regulator 61 is a two-stage type regulator which comprises a primary regulator (high-pressure regulator) 65a and a secondary regulator (low-pressure regulator) 65b. 
However, a single stage type regulator may be used if, for example, the gas fuel pressure is relatively low.
A throttle valve 66 is provided in the intake pipe 63. The throttle valve 66 opens and closes the intake pipe 63 according to an accelerator opening degree of the vehicle to adjust an amount of intake air. The injector 64 is provided at a downstream side of the throttle valve 66, i.e., a combustion chamber side of the engine, in the intake pipe 63.
The gas fuel is compressed to approximately 20 MPa (≈200 kgf/cm2) for example, and is put into the fuel tank. The fuel supplied to the high-pressure fuel supply passage 60 from the fuel tank is decompressed to approximately 390 kPa (≈3.9 kgf/cm2) by the high-pressure regulator 65a. Subsequently, the fuel is decompressed and regulated to approximately 30 kPa (≈0.3 kgf/cm2) by the low-pressure regulator 65b, and then supplied to the injector 64 through the low-pressure fuel supply passage 62.
In the meantime the high pressure and the low-pressure regulators 65a and 65b comprises valve elements 68a and 68b movable upwardly and downwardly to open and close passing holes 67a and 67b for the gas fuel, and diaphragms 69a and 69b to which the valve elements 68a and 68b are connected. Insides of the regulators 65a and 65b are divided into decompression chambers 70a and 70b and diaphragm chambers 71a and 71b. The decompression chambers 70a and 70b are defined in front sides of the diaphragms 69a and 69b and receive the gas fuel passing through the passing holes 67a and 67b. The diaphragm chambers 71a and 71b are defined in back sides of the diaphragms 69a and 69b. Adjustment springs 72a and 72b are provided in the diaphragm chambers 71a and 71b. The adjustment springs 72a and 72b are disposed in approximate central parts of the diaphragms 69a and 69b. The adjustment springs 72a and 72b urge the diaphragms 69a and 69b in such directions that the valve elements 68a and 68b open the passing holes 67a and 67b (downwardly in the figure).
The diaphragm chambers 71a and 71b are released to the atmosphere, and the pressure in the diaphragm chambers 71a and 71b is atmospheric pressure (approximately 0.1 MPa≈1 kgf/cm2). The gas fuel from the fuel tank flows into the decompression chambers 70a and 70b through the inlet holes 67a and 67b. When the gas fuel flows into the decompression chambers 70a and 70b, the pressure in the decompression chambers 70a and 70b rises. When the pressure in the decompression chambers 70a and 70b reaches a predetermined set pressure, the pressure in the decompression chambers 70a and 70b becomes greater than the resultant force of the pressure in the diaphragm chambers 71a and 71b (atmospheric pressure) and the urging force of the adjustment springs 72a and 72b. Accordingly, the diaphragms 69a and 69b and the valve elements 68a and 68b are pushed up and the inlet holes 67a and 67b are closed. When the gas fuel in the decompression chambers 70a and 70b flows out and the pressure in the decompression chambers 70a and 70b falls, the resultant force of the pressure in the diaphragm chambers 71a and 71b and the urging force of the adjustment springs 72a and 72b becomes greater than the pressure in the decompression chambers 70a and 70b. Accordingly, the valve elements 68a and 68b are pushed down and the inlet holes 67a and 67b are opened. As a result, the pressure of the gas fuel that is in and out of the decompression chambers 70a and 70b is kept almost constant.
That is, the pressure of the gas fuel flowing out of the regulators 65a and 65b is determined by a balance between a force for opening the inlet holes 67a and 67b (a force for pushing the diaphragms 69a and 69b and the valve elements 68a and 68b down) which is caused by a resultant of the pressure in the diaphragm chambers 71a and 71b (atmospheric pressure) and the urging force of the adjustment springs 72a and 72b, and a force for closing the inlet holes 67a and 67b (a force for pushing the diaphragms 69a and 69b and the valve elements 68a and 68b up) which is caused by the pressure of the gas fuel in the decompression chambers 70a and 70b. 
Therefore, the pressure of the fuel supplied to the injector 64 through the regulator 61 (injector source pressure) always becomes almost constant. Accordingly, an increase and decrease control of the fuel injection quantity is performed by the injector 64 in accordance with variation of a running condition of the vehicle (e.g., opening and closing of the throttle valve 66).
However, there has been a problem that, if the injector source pressure is always constant, a controllable range of the increase and decrease control of the fuel injection quantity becomes narrow and thus it becomes impossible to cope with an engine having a wide power range, since the minimum injection quantity and the maximum injection quantity of the fuel is determined by the performance of the injector 64. That is, if such an injector is adopted that has a superior controllability in an idle region where the fuel injection quantity is small, the maximum injection quantity of the fuel may lack. If such an injector is adopted that has a superior controllability in a high power region where the fuel injection quantity is large, the fuel injection quantity at the time of idling may become excessive and an idling speed may not be controlled.
In particular, the maximum fuel injection quantity of the fuel depends on the injector source pressure, and thus is limited if a control by the injector only is performed.